Given a database consisting of one first normal form relation FIRST with attribu

Question

Given a database consisting of one first normal form relation FIRST with attributes {A, B, C, D, E, F, G, H,I J and the functional dependencies as follows FIRST | A | B | C | D | E | F | G | H Functional Dependencies {AB -» C, BD EF, AD GH, A-I, H-J 1. Normalize FIRST into second normal form by giving the relation names, their attributes with primary keys underscored and foreign keys pointing to the corresponding attributes properly and its dependency diagrams as showing above (4 marks). 2. Normalize the result in the second question into the third normal form by giving the relation names, their attributes with primary keys underscored and foreign keys pointing to the corresponding attributes properly and its dependency diagrams as showing above (4 marks).

Explanation / Answer

AD -> GH (given) => ABD -> ABDGH (augmentation and reflexivity)

Since A->I (given) then ABD->ABDI (augmentation and reflexivity)

AB->C (given) => ABD->ABCD

BD->EF (given) => ABD->ABDEF

AD->GH (given) => AD->H. Since H->J then AD->J. Thus, ABD-> ABDJ.

Finally, using the union rule ABD->ABCDEFGHIJ.

So ABD is a key

1. Second normal form(2NF) :

=> satisfy condition of 1st Normal form.

=> All non prime attribute are fully functional dependent on any key of relation.

note:

-non prime attribute:

Attribute which is not a part of any key of a relation.

- Fully function dependency:

If x determines y ( x -> y )

then y can not be determined by any proper ssubsets of x.

R1 (A B C)

R2 (BD E F)

R3 (AD G H J)

R4 (A I)

2. Third normal form (3NF):

=> It is in second normal form.

=>All nonprimary fields are dependent on the primary key.

means there should not be the case that a non prime attribute is dependent on another non prime attribute.

R1 (AB C)

R2 (BD E F)

R3.1 (AD G H)

R4 (A I)

R3.2 (H J)

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